Axions from strings: the attractive solution

Abstract

We study the system of axion strings that forms in the early Universe if the Peccei-Quinn symmetry is restored after inflation. Using numerical simulations, we establish the existence of an asymptotic solution to which the system is attracted independently of the initial conditions. We study in detail the properties of this solution, including the average number of strings per Hubble patch, the distribution of loops and long strings, the way that different types of radiation are emitted, and the shape of the spectrum of axions produced. We find clear evidence of logarithmic violations of the scaling properties of the attractor solution. We also find that, while most of the axions are emitted with momenta of order Hubble, most of the axion energy density is contained in axions with energy of order the string core scale, at least in the parameter range available in the simulation. While such a spectrum would lead to a negligible number density of relic axions from strings when extrapolated to the physical parameter region, we show that the presence of small logarithmic corrections to the spectrum shape could completely alter such a conclusion. A detailed understanding of the evolution of the axion spectrum is therefore crucial for a reliable estimate of the relic axion abundance from strings. IntroductionThe QCD axion [1-7] is the simplest and most robust of the known solutions of the Standard Model (SM) Strong CP problem, and it also automatically forms a component of cold dark matter (DM) [8][9][10]. Consequently, a QCD axion that makes up the entire measured DM relic abundance is one of the best motivated scenarios for physics beyond the SM. In addition, numerous experiments aimed at detecting axions are currently running or in development. These will be sensitive to a substantial proportion of the relevant parameter space, and, if an axion is discovered, they could measure its mass and couplings precisely (see e.g. [11,12]).The dynamics by which QCD axion DM is produced, and its final relic abundance, depends on the cosmological history of the Universe (see e.g. [13,14]). If the Peccei-Quinn (PQ) symmetry that gives rise to the axion was broken after inflation, the axion field had initially random fluctuations over the present day observable Universe. Instead, if the PQ symmetry was broken during inflation and never subsequently restored, the axion field was initially homogeneous. In this case the axion relic abundance is incalculable because it depends on the local value of the axion field after inflation. 1 In this paper we study the class of models in which PQ breaking happens after inflation. This includes theories in which inflation happened at a scale above the axion decay constant f a , and also those with inflation at a lower scale but which were reheated to a temperature above f a . 2 In this case, assuming a standard cosmological history, the relic abundance is calculable in terms of the axion mass due to the random initial conditions. 3 . As a result, there is in principle a unique calculable predict...

Small-scale structure of fuzzy and axion-like dark matter

“…where θ 2 a,i is the initial squared misalignment angle averaged over our Hubble volume and F is a monotonic O(1) function of θ a that accounts for anharmonic corrections of the cosine potential. This is understood to be only a rough estimate; more refined predictions are the subject of active investigations [23,24,25,26].…”

“…Modern simulations therefore work with a variety of methods to maintain numerically resolved strings by making the mass of the radial mode explicitly time-dependent [195,196] or auxiliary fields to achieve higher effective string tensions [197]. Although it is understood that insufficient spatial resolution can lead to the unphysical decay of domain walls [24], current results indicate that the final axion yield depends only weakly on the numerical string tension [197]. The field remains very active.…”

Axion dark matter from Higgs inflation with an intermediate H*

“…In Fig. 2, we also show the expected reach of the haloscope searches [35,[159][160][161] by ADMX [162][163][164][165] and KLASH [166], which are also going to explore values of the axion mass that are lighter than what has been recently inferred by numerical computations of the dynamics of the PQ field [16][17][18][19]36] in a different cosmological scenario. On a theoretical viewpoint, the results obtained do not depend on the coupling of the QCD axion with the photons [167][168][169][170], which is nonetheless present when considering the experimental setup [171][172][173][174][175][176].…”

“…[8]. The level of precision reached in the assessment of the mass of the QCD axion and its dependence on the temperature of the QCD plasma from basic principles is quickly progressing, advancing in both extracting the QCD susceptibility from lattice computations [9][10][11][12] as well as in simulations of the string-wall network [13][14][15][16][17][18][19].…”

“…Other non-QCD axions that have been extensively considered in the literature as fields spectating inflation are the "ultra-light" axion particles which arise from string compactification, forming the so-called "axiverse" [43][44][45][46][47][48][49][50][51][52][53], and which can possibly be detectable when invoking axion electrodynamics. The opposite regime in which inflation occurs at a scale much higher than the energy at which the spontaneous breaking of the PQ symmetry occurs, H * v σ , has also received attention recently, with refined cosmological simulations set in the standard cosmological scenario yielding a narrow range in which the QCD axion would be the CDM particle [18,19,36].…”